Question 1: Yes, squats and pulls can go to TM programming while Bench/Press maintain AB novice rotation. No problem there.
Question 2: I equate it to this: "I want to lose weight, but I don't want to stop eating ice cream. Can you please give me a weight loss program that includes daily consumption of ice cream." That being said, do your HIIT conditioning on recovery day and Saturdays. Just pick something that doesn't make you sore.